It's worth getting in touch with Age Concern as they often have lists of places like Day Centres (some of which are still open or at least offering a service to the elderly). Day Centres are like clubs for the elderly. My mum, who had dementia, used to love her Day Centre. They had quizzes, craft things, chiropodist and hairdresser visits, visits from speakers. The members pay for each day they visit and are picked up (usually) in a mini van, lunch, coffee/tea and biscuits is included in the price at our local one. They're not cheap but if you're not going out anyway it's worth it.
Age Concern may also be able to offer more advice as they've dealt with these sort of issues for years.
Our local church used to provide visitor services - just someone to pop in once a week for a cuppa and a chat (not church related at all - just a visitor).
I used to live 10 minutes walk from my mum but only visited once a week, plus I covered endless appointments (almost 30 separate appointments in one year!) My mum was very intense and I found her quite draining - once a week sitting and chatting was all I could mentally cope with. I did ring a couple of times a week. It can be 'horses for courses' with family. Different personalities react differently. If it had been my dad I'd have probably been there more frequently as we were very similar in temperament. Doesn't mean I loved my mum any less than dad and would do anything for her but there were times a quick run to the loo for a silent scream kept me sane in her company!
As for the not making a cup of tea for your mum. We were advised by her doctor to not do 'stuff' for mum when we were at her flat. The more we did, the more she forgot. So when I helped change the bed, she'd do the pillows - the duvet is hard work for an 80 year old but she could do the pillows. It would take her more time to do them than for me to strip and remake the rest of the bed and get a wash on. But she was keeping that knowledge and that's important.
From a practical point of view, would someone like a domestic help be of use? Mum had a lady come in twice a week as she was struggling to keep everything clean with dementia (just forgot to wipe down the loo for example). And whilst we'd do everything we could to help her, covering cleaning, appointments, shopping whilst still finding time to sit and chat was hard. So we got a cleaner.
As she'd been diagnosed with dementia she was entitled to attendance allowance which can be used on anything to keep her world 'normal'. At first we used it to have a hairdresser visit, then it was domestic help, then it was more personal care. It's not means tested (or wasn't five years ago). That may be something you can look at - we also used it towards mum's Day Centre fees too. Even just getting someone in to clean once a week is company.
Mum decided, about a year before her dementia diagnosis, that she wanted to go into sheltered housing (she eventually went through extra care housing then care home as she became less able to do anything for herself - terrible disease). The sheltered housing was fantastic. Everything on site including a little restaurant and things like bingo, afternoon tea and biscuits downstairs just for a chat. That sort of thing. That may be something to broach once Covid is over. I wouldn't hesitate going into sheltered housing when I'm older - mum's place (council run) was lovely.
But do call Age Concern and, if she is having memory problems, it may be worth having a chat with the GP for an assessment.
As far as your sister is concerned, she is doing what she can. Caring for someone is hard and we're not all able to cope with it. Would she be able to help with other things, like organising shopping, arranging help around the house etc if (like me) she's better at the practical stuff? Take some of the pressure off you that way?